How do I animate a cube turning into a sphere when it is moved through a plane.
Parent cube and sphere to an empty. Put two additional cubes below and above the sphere. Use the upper one as a boolean to eat the cube, use the lower one to eat the sphere. Use the empty to animate them.

Here's the setting in one picture: The Empty moves cube and sphere up or down, 'cubekiller' and 'spherekiller' are simple cubes who touch each other. You can put them on a disabled layer or disable rendering in the Outliner.



The modifier settings are straightforward



And the result: